ON THE SEMIGROUP OF DIFUNCTIONAL BINARY RELATIONS

Authors

  • Muhammad Jamilu Ibrahim
    Department of Mathematics, Sule Lamido University Kafin Hausa Jigawa State Nigeria
  • Ibrahim Mamman Sawudi
    Department of Mathematics, Federal College of Education, Katsina
  • Abdussamad Tanko Imam
    Department of Mathematics, Ahmadu Bello University, Zaria

Keywords:

Binary relations, Cardinalities, Difunctional relations, Green’s relations

Abstract

In this paper, we have examine some properties of elements of the semigroup , where DX, is the set of all binary relations α ⊆ X × X satisfying , (), and is a binary operation on DX defined by () , with xα denoting set of images of x under α, and yβ−1 denoting set of pre-images of y under β. In particular, we showed that in the semigroup  there is no distinction between the concepts of reflexive and symmetric relations. We also presented a characterization of idempotent elements in  in term of equivalence relations.

Dimensions

East, J. and Vernitski, A. (2018): Ranks of ideals in inverse semigroups of difunctional binary relations. Semigroup Forum. 96, 21 – 30.

Jaoua, A., Elloumi, S., Hasnah, A., Jaam, J. and Nafkha, I. (2004): Discovering regularities in databases using canonical decomposition of binary relations. Journal on Relational methods in Computer Science. 1, 217 – 234.

Kudryavtseva, G. and Maltcev, V. (2011): Two generalizations of the symmetric inverse semigroup.

Publicationes Mathematicae Debrecen 78, 253 – 282.

Riguet, J. (1948): Relations binaire, fermetures, correspondances de galois. Bulletin Society Mathematics France. 76, 114 – 155.

Vernitski, A. (2007): A generalization of symmetric inverse semigroups. Semigroup Forum 75, 417 – 426.

Published

15-08-2022

How to Cite

Ibrahim, M. J., Sawudi , I. M., & Imam, A. T. (2022). ON THE SEMIGROUP OF DIFUNCTIONAL BINARY RELATIONS. FUDMA JOURNAL OF SCIENCES, 6(4), 17-19. https://doi.org/10.33003/fjs-2022-0604-1026

Issue

Vol. 6 No. 4 (2022): FUDMA Journal of Sciences - Vol. 6 No. 4

Section

Research Articles
Copyright & Licensing

How to Cite

Ibrahim, M. J., Sawudi , I. M., & Imam, A. T. (2022). ON THE SEMIGROUP OF DIFUNCTIONAL BINARY RELATIONS. FUDMA JOURNAL OF SCIENCES, 6(4), 17-19. https://doi.org/10.33003/fjs-2022-0604-1026